Linear Algebra Help - Subspaces

[WorthDaMoney]

So I have a test tomorrow and I just realized that I actually don't understand the concept of a subspace... I've checked in my textbook, my notes and online and i cant find an explanation that makes sense to me.
Anyone think they could explain it to me? Please don't try and explain unless you know for sure because I'm already confused and don't want to get even more confused.

 

[ClownPrince]

what exactly don't you understand? like what do you know about them, and what's unclear?
i mean, i can give you the definition but i'm sure you can find that yourself. if you tell me what exactly you don't understand, i think that would be better. like give me an example problem in a review or someting that you don't get.
i took linear algebra like a year ago, but maybe i can remember something.

 

[BootySpunk.]

Try here: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/

 

[WorthDaMoney]

for example:A subspace of R^m is a non-empty set of S, of vectors satisfying two conditions:1. If v1 is in S, and v2 is in S, then v1+v2 is in S2. If V is in S, and c is a scalar, then cV is in S
thats the definition i was given. so what does "in S" mean? i think thats where i get lost

 

[ClownPrince]

my bad, i completely forgot about this. i hope this still helps.
i'm pretty sure S is the subspace itself here.
so the first thing it's telling you is that S is a set. that means there are things in S (nonempty), and those things are vectors (in Rm).
then, the definition gives you two axioms ("subspace axioms"). what that means is that a subset fulfilling these conditions is a special kind of subset (a subspace).
so in order to show that S (which you already know is a subset by definition) is a subspace, you just show that for all the vectors in S (which are also in Rm, which S is a subset of), (1) and (2) are true.
so all a subspace is is just a type of vector space, that's "closed" under the two axioms and contains some vectors in Rm. you kinda just have to memorize that.
hopefully this helps. any more questions, i'll try to answer or clarify.

 

[zerospinskier]

http://www.khanacademy.org/
Go here and go to the Linear Algebra section. I guarantee you won't find a better person to explain it to you. He is so easy to understand it is crazy.